Ocean spectral data assimilation without background error covariance matrix

Abstract

Predetermination of background error covariance matrix B is challenging in existing ocean data assimilation schemes such as the optimal interpolation (OI). An optimal spectral decomposition (OSD) has been developed to overcome such difficulty without using the B matrix. The basis functions are eigenvectors of the horizontal Laplacian operator, pre-calculated on the base of ocean topography, and independent on any observational data and background fields. Minimization of analysis error variance is achieved by optimal selection of the spectral coefficients. Optimal mode truncation is dependent on the observational data and observational error variance and determined using the steep-descending method. Analytical 2D fields of large and small mesoscale eddies with white Gaussian noises inside a domain with four rigid and curved boundaries are used to demonstrate the capability of the OSD method. The overall error reduction using the OSD is evident in comparison to the OI scheme. Synoptic monthly gridded world ocean temperature, salinity, and absolute geostrophic velocity datasets produced with the OSD method and quality controlled by the NOAA National Centers for Environmental Information (NCEI) are also presented.

Synoptic monthly gridded global and regional four‐dimensional World Ocean Database and Global Temperature and Salinity Profile Programme (T, S, u, v) fields with the optimal spectral decomposition and P‐vector methods

“…The OSD method (Chu et al ., ,b, , , ), used to produce SMG‐( T , S ) datasets, can be outlined as follows. Let r = ( x , y ) be the horizontal coordinates and z the vertical coordinate.…”

“…In producing the SMG‐WOD and SMG‐GTSPP ( T , S ) data, around 30 basis functions are used. The OSD data assimilation equation is given by (Chu et al ., ) where F is an N × N diagonal observational contribution matrix …”

“…In producing the SMG-WOD and SMG-GTSPP (T, S) data, around 30 basis functions are used. The OSD data assimilation equation is given by (Chu et al, 2016)…”

“…The OSD method has been proven an effective ocean data analysis method (Chu et al, 2016). With it, several new ocean phenomena have been identified from observational data such as a bimodal structure of chlorophyll-a with winter/spring (February-March) and fall (September-October) blooms in the Black Sea (Chu et al, 2005a), fall-winter recurrence of current reversal from westward to eastward on the Texas-Louisiana continental shelf from the current meter, near-surface drifting buoy (Chu et al, 2005b), propagation of long Rossby waves at mid-depths (around 1000 m) in the tropical North Atlantic from the Argo float data (Chu et al, 2007), and temporal and spatial variability of global upper ocean heat content (Chu, 2011).…”

The 47th Liege Colloquium: marine environmental monitoring, modelling and prediction

“…First, assimilation schemes and systems were discussed and presented during the colloquium, for instance the OpenDA assimilation system coupled with NEMO (van Velzen et al 2016) and more theoretical work on the implicit definition of error covariance matrix (Chu et al 2016) and local assimilation scheme with global constraints and conservation (Barth et al 2016). The collection includes also several studies of data assimilation with realistic ocean models.…”